학술논문
Archetypal analysis for ordinal data.
Document Type
Journal
Author
Fernández, Daniel (E-UPB-OR) AMS Author Profile; Epifanio, Irene (E-JAU) AMS Author Profile; McMillan, Louise Fastier (NZ-VCTR-SMS) AMS Author Profile
Source
Subject
62 Statistics -- 62H Multivariate analysis
62H17Contingency tables
62H17
Language
English
Abstract
Summary: ``Archetypoid analysis (ADA) is an exploratory approach thatexplains a set of continuous observations as mixtures of pure (extreme)patterns. Those patterns (archetypoids) are actual observations of thesample which makes the results of this technique easily interpretable,even for non-experts. Note that the observations are approximated as aconvex combination of the archetypoids. Archetypoid analysis, in itscurrent form, cannot be applied directly to ordinal data. We proposeand describe a two-step method for applying ADA to ordinal responsesbased on the ordered stereotype model. One of the main advantages ofthis model is that it allows us to convert the ordinal data tonumerical values, using a new data-driven spacing that better reflectsthe ordinal patterns of the data, and this numerical conversion thenenables us to apply ADA straightforwardly. The results of the novelmethod are presented for two behavioural science applications. Finally,the proposed method is also compared with other unsupervisedstatistical learning methods.''